S_|0,4}

[koh]

    Max.

    Thanks for your "detective" work of  S_{0,4}.
    I feel sorry that the criminal is still running away.

    If the term becomes a number n of the form {2^k*l^2*p^(2*r+1), GCD(2,l)=1, GCD(l,p)=1, p is prime, Sigma(p^(2*r+1)=2*t, GCD(2,t)=1} or {2^k*l^2, GCD(2,l)=1} then Sigma(n)=2*u or u, GCD(2,u)=1, so it becomes end.
    But I don't know how to calculate the probability that a number becomes of this form.

    Once I tried to experiment starting with many numbers and I remember that if numbers are large enough then they almost all seem to go to infinity.
    I am not sure how many digits they need but probably 10^15<n.
 
    I think that the sequence starting with  n=555500000011111 which ends after only 10 iterations is rather rare case.

    Finding {0,4}-Aliquot cycles is also interesting.
    I calculated several solutions.
    See MathWorld.

         http://mathworld.wolfram.com/SociableNumbers.html
    
    If you have time to search them, try it.
    And if you got the examples, tell me them.
 

    Neil

    T_{0,4} : b(1)=5500000011111, b(n)=1/4*Sigma(b(n-1)) 

    I think that T_{0,4} is interesting.
    But I don't think that you add it to OEIS.
    I suppose that one of the "Raison d'etre" of OEIS is identification of sequences.
    If some one starts b(n) with a different number from 5500000011111 then OEIS never identifies it.
    Tell me how to make it a "good" sequence which fits to OEIS.

    Yasutoshi